Can water simply absord the kinetic energy from colliding air molucules to change its phase? And can water transformed into ice simply have the kinetic energy of its molecules increased to balance out the lost latent heat? Would not this again change ice into water?
Latent heat is the heat released or absorbed in connection with a phase change. The term "latent" means hidden or concealed because heat transfer is normally associated with temperature change, whereas latent heat transfer does not involve temperature change.
Can water simply absord the kinetic energy from colliding air molucules to change its phase?
Yes if the temperature of the air is greater than the boiling point of water. Then latent heat transfer from the air molecules to the water can cause a phase change, i.e., convert the water from a liquid to a gas. The air molecules lose kinetic energy while the water molecules gain an equal amount of potential energy due to separation of the water molecules, since the temperature (and thus kinetic energy) of the water molecules is constant during the phase change.
And can water transformed into ice simply have the kinetic energy of its molecules increased to balance out the lost latent heat?
Once again a phase change of water from ice to water does not involve a change in the internal kinetic energy of the water since it occurs at constant temperature. The air (or whatever the source of heat) loses kinetic energy while the latent heat transfer to the ice involves an equal increase in the internal potential energy of the water due to separation of the water molecules. An analogy is the increase in gravitational potential energy of an object when separated from the surface of the earth in opposition to the gravitational force.
By the way, regarding the title of your post, the primary heat transfer between the air and the water or ice would most likely be convection, and not radiation.
Hope this helps.